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PCAs the choices above demonstrate, most T206s are really nice, which is one of the reasons the set is so popular. There are so many great cards, that I think you'll find more of a consensus on the few "odd" looking poses.
Since you are looking for action shots, maybe limit yourself to a throwing pose or a pitching pose, with a sunset background. Just about any three of those cards, framed in a row, will look great. Then, do a bunch of searches on eBay, and find three that are lower condition and within your price range, but present well (no heavy creases). Maybe look for cards with heavy back damage, but nice fronts.
You can do the same thing with three T206 portraits, with the same background color, or red-yellow-orange, etc.
Just don't permanently mount the cards in the frame! With enough backing, the cards should stay put without having to be glued.